The positron lifetime and the Doppler-broadening of the annihilation radiation have been investigated in high-purity uranium at temperatures between 290 K and 1400 K. We find a significant dependence of the bulk lifetime and the annihilation lineshape on crystal structure and on temperature. Trapping at vacancies is observed only in γ-uranium. The total trapping rate is surprisingly low and increases by only a factor of two from the β → γ transition temperature to the melting point. In γ-uranium... »